Preparation

For pesto:
Blend mint leaves, pistachios, olive oil, and garlic in processor until coarse puree forms. Season with coarse salt. DO AHEAD Can be made 1 day ahead. Cover and chill. Bring pesto to room temperature and stir before using.

For fish:
Combine olive oil, mint, and thyme in small bowl. Spread herb mixture all over both sides of fish fillets. Cover and refrigerate fish at least 3 hours and up to 5 hours.

For spiced carrots:
Stir all seeds in small dry skillet over medium heat until fragrant, about 2 minutes. Transfer seeds to spice mill or mortar and grind coarsely.

Heat 1 tablespoon oil in heavy large skillet over medium-high heat. Add carrots, crushed red pepper, and ground seeds; sauté until carrots begin to brown in spots, about 5 minutes. Add broth and lemon juice and bring to boil. Reduce heat to medium-low, cover, and simmer until carrots are tender, about 6 minutes. Season to taste with salt and pepper. DO AHEAD Can be made 2 hours ahead. Let stand at room temperature.

Sprinkle fish with salt and pepper. Heat 1 tablespoon oil in each of 2 large nonstick skillets over medium-high heat. Add fish and cook until browned on both sides and just opaque in center, about 5 minutes total.

Rewarm carrots just until heated through. Divide carrots and any juices among 4 plates. Top each serving with 1 fish fillet. Spoon pesto over and serve.